Development of a physical theory of plasticity

Abstract

A physical theory of plasticity is developed from the slip theory given by Lin and his associates. In this slip theory, a large region composed of innumerous identical cubic blocks of 27 differently oriented face-centered-cubic crystals is embedded in an infinite isotropic elastic medium. Loading is applied to the infinite medium. The stress and strain fields in the center block is calculated using the analogy between plastic strains and applied force. These fields satisfy the conditions of equilibrium and continuity of displacement throughout the block. The average stress and strain of this block is considered to represent the macro-stress-strain of the metal. The 27-crystal model gives some plastic shear strain under tensile loading that does not agree with test data. In this paper a 64-crystal model is used. These crystals are arranged to give symmetry about 3 orthogonal planes and same crystal orientations relative to the three perpendicular axes. With this model, the undesirable plastic shear strain is removed. Significant simplifications in the numerical calculations have been developed.Calculations by this theory have been made on an aluminum alloy subject to three different ratios of incremental axial and torsional loadings after being compressed beyond the elastic range. These calculated results agree with experimental data in a thin wall cylinder, considerably better than the commonly used flow and deformation theories of plasticity. Lode parameters of strain were calculated for different Lode parameters of stress. These calculated results again agree considerably better than the commonly used mathematical theories of plasticity.